Not necessarily. Unless some hot-headed Southern officer finds another way to start the war, this may end up in the South's favor. Confederate diplomats in Washington in 1861 warned Davis not to fire the first shot. If they hold out long enough, public support in the North for a war would be far lower, and Lincoln will have no choice but to compromise with them. Unless he starts a fight, in which case his popularity will plummet when he calls for troops from across the nation, and you have a repeat of the Nullification Crisis.